University of Technology, Sydney · My UTS colleagues whose advice, humour, and knowledge has helped me focus and provided entertainment through this journey. Salisa Abdulrahman,

UTS University of Technology, Sydney

Faculty of Engineering and Information Technology

Synchroniser analysis and shift dynamics of powertrains

equipped with dual clutch transmissions

A thesis submitted for the degree of

Doctor of Philosophy

Paul David Walker

July 2011

CERTIFICATE OF ORIGINALITY

I certify that the work in this thesis has not previously been submitted for a degree nor

has it been submitted as part of requirements for a degree except as fully acknowledged

within the text.

I also certify that the thesis has been written by me. Any help that I have received in my

research work and the preparation of the thesis itself has been acknowledged. In

addition, I certify that all information sources and literature used are indicated in the

thesis.

Paul David Walker

July 2011

11

ACKNOWLEDGEMENTS

I'd like to take this opportunity to thank the following people for their assistance and

support during my candidature.

My supervisor Professor Nong Zhang, his knowledge and guidance has been invaluable,

and together with eo-supervisors Dr Jeku Jeyakumaran and Dr Jinchen Ji have guided

me through this research and supported my work.

The team at NTC Powertrains - Ric Tamba and Simon Fitzgerald - whose ideas

imitated this project and provided information critical to the success of this work.

My UTS colleagues whose advice, humour, and knowledge has helped me focus and

provided entertainment through this journey. Salisa Abdulrahman, Yoo-shin Kim,

Robert Heal, Lifu Wang, Nga Hoang, Jin Zhang, Jing Zhao and many others along the

way.

Most importantly, my wife, Hoeun, who stuck with me through thick and thin, I

couldn't have done this without you babe; and daughter, Abbygail, my pride and joy.

My parents, Gary and Sue, for advice, and sister, Leigh, and brother, Ryan for

entertainment.

Financial support for this project is provided jointly by the Australian Research Council

(Linkage ID number LP0775445) and NTC Powertrains.

iii

TABLE OF CONTENTS

ACKNOWLEDGEMENTS ............................................................................................... ii

TABLE OF CONTENTS ................................................................................................... iii

LIST OF FIGURES ........................................................................................................... xi

LIST OF TABLES ........................................................................................................ xviii

GLOSSARY OF TERMS AND NOTATION ............................................................. xix

ABSTRACT ................................................................................................................... xxviii

CHAP'fER 1: INTRODUCTION ............................................................................. !

1.1 PROJECT STATEMENT .................................................................................. 2

1.2 PROJECT OBJECTIVES ................................................................................... 3

1.3 PROJECT SCOPE .............................................................................................. 3

1.4 PRESENTATION OF THIS THESIS ................................................................ 3

1.5 PUBLICATIONS ............................................................................................... 8

CHAP'fER 2: BACKGROUND INFORMATION AND LITERATURE

REVIEW ············································································································· 9

2.1 INTRODUCTION .............................................................................................. 9

2.2 BACKGROUND INTO DCT EQUIPPED POWER TRAINS .......................... 9

2.2.1 Powertrains ................................................................................................ 10

2.2.2 Engine ....................................................................................................... 10

2.2.3 Flywheel .................................................................................................... 11

2.2.4 The dual clutch transmission ..................................................................... 11

2.2.5 Powertrain nonlinearities .......................................................................... 12

2.2.6 Synchroniser and drag torque ................................................................... 13

2.2.7 Control systems ......................................................................................... 14

2.2.8 Drivetrain and differential.. ....................................................................... 15

2.3 DCT POWERTRAINS, SIMULATIONS, MODELLING AND CONTROL 15

2.3.1 Designs and state-of-the-art ...................................................................... 15

2.3.1.1 Wet Vs Dry clutches .......................................................................... 15

2.3.1.2

2.3.1.3

iv

Electro-hydraulic or electromechanical control systems ................... 16

Applications ....................................................................................... 17

Modelling, simulations, and analysis ........................................................ 17

Control methods employed in DCTs ........................................................ 18

2.3.2

2.3.3

2.3.4 Assumptions and limitations of current research ...................................... 20

2.3.4.1

2.3.4.2

2.3.4.3

2.3.4.4

2.3.4.5

2.3.4.6

Hydraulic control system models ...................................................... 20

Engine torque models ........................................................................ 22

Synchroniser ...................................................................................... 22

Gear mesh nonlinearities ................................................................... 23

Temperature ....................................................................................... 23

Mechanical losses .............................................................................. 24

2.3.5 A final note on DCT control and assumptions .......................................... 24

2.3.6 Synchroniser dynamics and modelling ..................................................... 25

2.3.6.1 Fundamental studies of synchronisers ............................................... 25

2.3.6.2 Failure modes in the synchroniser ..................................................... 26

2.3.6.3 Numerical simulations of synchronisers ............................................ 28

2.3.7 Drag torque ............................................................................................... 31

2.3.7.1 Simulations of combined drag torques .............................................. 32

2.3.7.2 Sources of drag .................................................................................. 32

2.3. 7.3 A final note on drag torque ................................................................ 34

2.3.8 Hydraulics ................................................................................................. 34

2.3.9 Engine models ........................................................................................... 35

2.3.10 Dual Mass Flywheel. ................................................................................. 36

2.3.11 Powertrain modelling methods ................................................................. 37

2.3.12 Powertrain control ..................................................................................... 38

2.3.13 Backlash modelling ................................................................................... 38

2.4 SUMMARY AND CONCLUSION ................................................................. 39

CHAPTER 3: HYDRAULIC CONTROL SYSTEM MODELLING AND

ANALYSIS ........................................................................................................... 41

3.1 INTRODUCTION ............................................................................................ 41

3.2 BACKGROUND .............................................................................................. 42

3.3 DEVELOPMENT OF HYDRAULIC SYSTEM MODELS: GENERAL MODEL FORMULATION ......................................................................................... 43

V

3.4 DEVELOPMENT OF HYDRAULIC SYSTEM MODELS: SOLENOID AND CLUTCH HYDRAULICS .......................................................................................... 47

3.5 SIMULINK® MODELLING AND INITIAL RESULTS ............................... 54

3.5.1 Solenoid response to basic inputs: Step .................................................... 51

3.5.2 Solenoid response to inputs: Ramp ........................................................... 59

3.5.3 Combined system response to inputs: Step ............................................... 59

3.5.4 Combined system response to inputs: Ramp ............................................ 63

3.6 DEVELOPMENT OF HYDRAULIC SYSTEM MODELS: SYNCHRONISER ...................................................................................................... 64

3.7 MATLAB MODELLING AND INITIAL RESULTS ..................................... 67

3.8 CHAPTER SUMMARY ANDCONCLUSION .............................................. 69

3.8.1 Summary of contributions ......................................................................... 70

CHAPTER 4: SYNCHRONISER MECHANISM RIGID BODY MODELLING

AND ANALYSIS ........................................................................................................... 72

4.1 INTRODUCTION ............................................................................................ 72

4.2 BACKGROUND .............................................................................................. 72

4.3 PROCESS DESCRIPTION .............................................................................. 74

4.3.1 Important considerations for synchronisers .............................................. 76

4.3.1.1 Failure modes ..................................................................................... 76

4.3.1.2 Limitations to design parameters ....................................................... 77

4.3.1.3 Multi-cone Synchronisers .................................................................. 78

4.3.1.4 Cone friction coefficient and materials .............................................. 79

4.4 DCT APPLICATION AND COMPARISON TO MANUAL TRANSMISSION ....................................................................................................... 79

4.5 MODEL DEVELOPMENT ............................................................................. 80

4.5.1 Model Parameters and initial conditions ................................................... 92

4.6 NUMERICAL SIMULATIONS ...................................................................... 93

4.6.1 Basic simulations ...................................................................................... 93

4.6.2 Up and down shift synchronisations for all gears ..................................... 95

4.6.3 Variation of chamfer alignment ................................................................ 97

4.6.4 Effect of varying sleeve rotational speed .................................................. 98

4.6.5 Influence of maximum hydraulic pressure ................................................ 99

4.6.6 Simulations with varied nominal transmission temperature ................... 100

4.6.7 Summation of simulation results ............................................................. l01

vi

4.7 DIMENSIONLESS TORQUE ANALYSIS .................................................. 102

4.8 DESIGN PARAMETER STUDY .................................................................. 107

4.9 CHAPTER SUMMARY AND CONCLUSION ............................................ 111

4.9.1 Summary of contributions ....................................................................... 112

CHAPTER 5: DRAG TORQUE MODELLING AND ANALYSIS •...•.•.•.•••..... 113

5.1 INTRODUCTION AND BACKGROUND ................................................... 113

5.2 SOURCES OF DRAG .................................................................................... 114

5.3 EFFECTS OF DRAG ..................................................................................... 115

5.4 DRAG TORQUE MODELLING ................................................................... 117

5.4.1 Bearing drag ............................................................................................ 117

5.4.2 Gear tooth friction drag ........................................................................... 118

5.4.2.1 Gear tooth friction coefficient ......................................................... 119

5.4.3 Gear windage drag .................................................................................. 120

5.4.4 Wet Clutch drag ...................................................................................... 122

5.4.5 Concentric shaft drag .............................................................................. 124

5 .4.6 Summary of modelling methods ............................................................. 124

5.4.7 Drag torque modelling parameters .......................................................... 125

5.5 APPLICATION TO THE DCT FOR DYNAMICS MODELS ..................... 125

5.5.1 Linearisation of drag torques for finite element models ......................... 126

5.6 APPLICATION TO THE SYNCHRONISER ............................................... 129

5 .6.1 Model verification ................................................................................... 131

5.6.2

5.6.2.1

5.6.2.2

Numerical simulations of drag torque ..................................................... 135

Breakdown of drag torques .............................................................. 135

Drag torque variation between gears ............................................... 137

5.7 CHAPTER SUMMARY AND CONCLUSION ............................................ 139


CHAPTER 6: POSITIVE CONTROL OF DETRIMENTAL CHAMFER

ALIGNMENTS IN SYNCHRONISERS .................................................................. 141

6.1 INTRODUCTION .......................................................................................... 141

6.2 CONTROL OF DETRIMENTAL CHAMFER ALIGNMENT .................... 142

6.2.1 Baseline simulations ............................................................................... 143

6.3 FEEDBACK CONTROL OF THE SYNCHRONISER ................................ 146

6.3.1 Simulations .............................................................................................. 147

vii

6.4 DISTURBANCE METHOD SIMULATIONS .............................................. 151

6.4.1 Case 1: Externally applied torque ........................................................... 152

6.4.2 Case 2: Impulse from inertia change ....................................................... 155

6.5 MINIMISATION OF SLIP REGENERATION ............................................ 159

6.6 CONCLUSIONS ............................................................................................ 162


CHAPTER 7: INVERTED SYNCHRONISER MECHANISM DESIGN ........ 164

7.1 INTRODUCTION .......................................................................................... 164

7.2 RATIONALE FOR SYNCHRONISER IMPROVEMENTS ........................ 164

7.3 IMPACT OF INCREASING CONE RADIUS .............................................. 165

7.4 CHAMFER DESIGN IMPROVEMENTS .................................................... 168

7.5 THE INVERTED CONE DESIGN ................................................................ 172

7.5.1 Simulations .............................................................................................. 174

7.6 CONCLUSIONS ............................................................................................ 177


CHAPTER 8: DYNAMIC MODELLING OF A DCT POWERTRAIN WITH

INTEGRATED SYNCHRONISERS ........................................................................ 179

8.1 INTRODUCTION .......................................................................................... 179

8.2 LUMPED MASS MODELLING THEORY AND APPLICATION ............. 180

8.2.1 Free vibration analysis ............................................................................ 181

8.2.1.1 Undamped free vibration ................................................................. 181

8.2.1.2 Damped free vibration ..................................................................... 182

8.3 POWERTRAIN STATES .............................................................................. 183

8.4 POWERTRAIN MODEL ............................................................................... 185

8.4.1 Engine, flywheel and clutch drum models .............................................. 186

8.4.2 Dual mass flywheel ................................................................................. 187

8.4.3 Transmission and synchroniser model .................................................... 189

8.4.4 Final drive ............................................................................................... 191

8.4.5 Propeller shaft model .............................................................................. 192

8.4.6 Differential, axle, and wheels and tyre models ....................................... 192

8.4.7 Model Parameters .................................................................................... 194

8.5 LUMPED INERTIA MODEL MATRICES AND FREE VIBRATION ANALYSIS ............................................................................................................... 196

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8.5.1 DAMPED FREE VIBRATION ANALYSIS ......................................... 196

8.6 MODELLING INPUT TORQUES ................................................................ 200

8.6.1 Engine models ......................................................................................... 200

8.6.1.1 Mean torque model .......................................................................... 200

8.6.1.2

8.6.1.3

8.6.2

8.6.3

Hannonic engine torque model ....................................................... 201

Hannonic engine control method .................................................... 203

Clutch torque model ................................................................................ 205

Synchroniser model. ................................................................................ 206

8.6.4 Vehicle torque model .............................................................................. 208

8.7 CHAPTER SUMMARY AND CONCLUSIONS ......................................... 208

8.7 .1 Summary of contributions ....................................................................... 210

CHAPTER 9: SHIFT CONTROL OF DCTS- ISSUES AFFECTING SHIFT

QUALITY ......................................................................................................... 211

9.1 INTRODUCTION .......................................................................................... 211

9.2 SHIFT CONTROL OF DUAL CLUTCH TRANSMISSIONS ..................... 212

9.2.1 Power shifting process in a DCT ............................................................ 212

9 .2.2 Shift requirements ................................................................................... 213

9.3 4/3 DOF MODELLING OF THE POWER TRAIN FOR CLUTCH CONTROL 214

9.3.1 Integration with hydraulic control system .............................................. 217

9.3.2 Parameter estimation ............................................................................... 218

9.3.3 Free vibration analysis ............................................................................ 221

9.4 TORQUE BASED CONTROLLER DEVELOPMENT FOR THE DCT ..... 224

9.4.1 Sensitivity of controller to estimated torque ........................................... 225

9.4.2 Torque orientated clutch control ............................................................. 225

9.4.2.1 Preshift control.. ............................................................................... 227

9.4.2.2 Torque phase control ....................................................................... 227

9 .4.2.3 Inertia phase control ........................................................................ 228

9.4.3 Alternate engine control methods ........................................................... 228

9.5 GENERAL SIMULATION CONTROL SIGNAL RESULTS ...................... 231

9.6 BASIC TORQUE ORIENTATED SHIFTING ............................................. 233

9 .6.1 Simulations with ideal actuators ............................................................. 233

9.6.2 Simulations with basic control methodology .......................................... 235

IX

9.6.3 Simulations with addition of engine torque control.. .............................. 237

9 .6.4 Simulations of the influence of error in torque estimation ..................... 238

9.6.5 Shift transient simulations with transient engine model ......................... 239

9.7 COMPENSATION FOR TIME DELAY IN HYDRAULIC CONTROL SYSTEM ................................................................................................................... 241

9.8 CONCLUSIONS ............................................................................................ 242

9 .8.1 Summary of Contributions ...................................................................... 244

CHAPTER 10: SHIFT TRANSIENT STUDY OF DCT EQUIPPED

POWER TRAINS ........................................................................................................ 245

10.1 INTRODUCTION .......................................................................................... 245

10.2 DYNAMICS OF SYNCHRONISER ENGAGEMENT IN A DCT POWER TRAIN ......................................................................................................... 245

1 0.2.1 Modified synchroniser model ................................................................. 246

10.2.2 Comparison of rigid body and lumped mass models for analysis .......... 246

10.2.3 Transient simulations with ideal engine torque model ........................... 248

10.2.4 Transient simulations with unsteady engine model ................................ 251

10.2.5 Comparison of responses during synchronisation for steady and unsteady engine models ........................................................................................................ 253

10.3 DYNAMICS OF POWER-ON CLUTCH-TO-CLUTCH SHIFTS IN A DCT POWER TRAIN ......................................................................................................... 255

10.3.1 Comparison of 4DOF and 15DOF models ............................................. 257

10.3.2 Application of transient engine torque model.. ....................................... 259

10.3.3 Inclusion ofDMFW ................................................................................ 261

10.4 THE COMBINED SYNCHRONISER ENGAGEMENT AND SHIFTING IN A DCT POWER TRAIN ............................................................................................ 262

10.5 CONCLUSIONS ............................................................................................ 267

10.5.1 Simulations of synchroniser engagement ............................................... 267

10.5 .2 Simulations of Shift transient.. ................................................................ 268

10.5.3 Simulations of combined synchronisation and gear shift ....................... 269


CHAPTER 11: TRANSIENT SIMULATIONS WITH BACKLASH IN GEARS

AND SYNCHRONISER ............................................................................................. 270

11.1 INTRODUCTION .......................................................................................... 270

11.2 MESH NONLINEARITIES ........................................................................... 271

X

11.2.1 Clonk ....................................................................................................... 271

11.3 MODIFICATIONS TO LUMPED INERTIA MODEL ................................ 272

11.3.1 Backlash model ....................................................................................... 274

11.3.2 Model parameters .................................................................................... 275

11.4 SIMULATIONS ............................................................................................. 276

11.4.1 Synchroniser Engagement.. ..................................................................... 277

11.5 SHIFf TRANSIENT WITH GEAR AND SYNCHRONISER BACKLASH ....

························································································································ 280

11.6 TIP-IN TIP-OUT OF THROTTLE ................................................................ 282

11.6.1 Throttle tip-in/tip-out modelling ............................................................. 283

11.6.2 Mean torque model simulations .............................................................. 284

11.6.3 Transient engine vibration and DMFW .................................................. 286

11.7 CONCLUSIONS ............................................................................................ 288


CHAPTER 12: THESIS CONCLUSIONS AND RECOMMENDATIONS ..••..• 290

12.1 SUMMARY OF THESIS ............................................................................... 290

12.2 SUMMARY OF FINDINGS AND CONTRIBUTIONS ............................... 291

12.3 LIMITATIONS TO RESEARCH .................................................................. 295

12.4 FURTHER RESEARCH ................................................................................ 296

12.5 CONCLUSION .............................................................................................. 298

APPENDIX A- UNBLOCKING TIME .....•.....•.........•..•••.••••.••........•....•••....•.•..•...... 300

APPENDIX B- DISPLACEMENT DERIVATION ............................................... 301

APPENDIX C- MATRIX EQUATIONS OF MOTION FOR POWERTRAIN

MODEL ......................................................................................................... 302

REFERENCES ......................................................................................................... 313

xi

LIST OF FIGURES

Figure 1.1: Relationship of different Chapter components of this thesis ..................................................... 4

Figure 2.1: General DCT powertrain layout ............................................................................................... 10

Figure 2.2: Dual lay shaft dual clutch transmission, where "C" represents clutches, "B" signifies bearing,

"G" is for a gear pair, and "S" identifies synchronisers ............................................................................. 12

Figure 2.3: Typical synchroniser mechanism schematic ............................................................................ 14

Figure 2.4: Mesh phases during indexing of the synchroniser [65] ........................................................... 29

Figure 2.5: Figure of sleeve displacement with varying chamfer alignments from Liu &Tseng [60] ....... 31

Figure 3.1: Single degree of freedom mass with damping ......................................................................... 43

Figure 3.2: Detail of flow area for open port .............................................................................................. 45

Figure 3.3: Schematic of clutch control system ......................................................................................... 48

Figure 3.4: Variable force solenoid schematic with integrated damper ..................................................... 48

Figure 3.5: Solenoid and damper control volumes ..................................................................................... 49

Figure 3.6: Schematic of clutch pack and piston ........................................................................................ 52

Figure 3.7: Clutch pack control volume ..................................................................................................... 52

Figure 3.8: Nonlinear spring model for clutch pack ................................................................................... 53

Figure 3.9: Characteristic Curve for VFS ................................................................................................... 55

Figure 3.10: Spool displacement and time delay for VFS ......................................................................... 55

Figure 3.11: Solenoid release spool displacement and time delay curves for step down ........................... 56

Figure 3.12: Normally low VFS response to step input ............................................................................. 57

Figure 3.13: Normally high VFS response to step input ............................................................................ 58

Figure 3.14: VFS response to ramp input. .................................................................................................. 59

Figure 3.15: Hydraulic system response to step input for clutch 1, l=0.6A ............................................... 60




Figure 3.19: Simulation of clutch 1 and VFS combined using a ramp input ............................................. 63

Figure 3.20: Hydraulic shift mechanisms for the DCT synchroniser control including four on/off

solenoids and a sequencing solenoid .......................................................................................................... 65

Figure 3.21: Hydraulic shift arrangement for typical DCT synchronisers ................................................. 66

Figure 3.22: Solenoid output pressure and cylinder response pressure ...................................................... 68

Figure 3.23: Idle cylinder response pressure .............................................................................................. 68

Figure 4.1: Steps of synchroniser engagement.. ......................................................................................... 76

xii

Figure 4.2: Typical transmission Layout for DCT, including synchronisers .............................................. 80

Figure 4.3: Simplified synchroniser model components for drag and inertia, studying 4th gear ................. 81

Figure 4.4: Ring free body diagram during speed synchronisation ............................................................ 86

Figure 4.5: Possible variations in chamfer alignment.. ............................................................................... 90

Figure 4.6: Resultant forces on the chamfers .............................................................................................. 91

Figure 4.7: Synchronisation process modelling summary .......................................................................... 91

Figure 4.8: Synchronisation process breakdown, showing cone slip speed (top), sleeve displacement

(middle), and hydraulic pressure (bottom) .................................................................................................. 94

Figure 4.9: Up shift synchroniser engagement simulations for all gears, (left) sleeve displacement of gears

2-6 with sleeve speed of 1500RPM, (right) duration for each step ............................................................. 95

Figure 4.10: Sleeve displacement for downshifts of gears 1-5 with sleeve speed of 1500RPM ................. 96

Figure 4.11: Demonstration of variation associated with chamfer alignment ............................................ 97

Figure 4.12: Variation in chamfer alignment simulations focusing on indexing only ................................ 97

Figure 4.13: Influence of sleeve speed on engagement for a 3'd -4th gear upshift synchronisation ............ 99

Figure 4.14: 3rd -4th gear upshift synchronisation with variations in control pressure from 0.4-2MPa, (a)

cylinder pressure and (b) sleeve displacement.. .......................................................................................... 99

Figure 4.15: Sleeve displacement with variation in ambient transmission temperature ........................... 101

Figure 4.16: Cone slip speed with variation in ambient transmission temperature ................................... 101

Figure 4.17: Dimensionless cone torque ................................................................................................... l04

Figure 4.18: Dimensionless blocking/indexing torque ............................................................................. 1 05

Figure 4.19: Dimensionless drag torque for downshifts ........................................................................... } 06

Figure 4.20: Dimensionless drag torque for up shifts ............................................................................... } 06

Figure 4.21: Parameter modification to cone angle .................................................................................. 108

Figure 4.22: Parameter modification to friction coefficient... ................................................................... 109

Figure 4.23: Chamfer angle parameter modification ................................................................................ 110

Figure 4.24: Parameter modification to chamfer friction .......................................................................... l10

Figure 5.1: DCT transmission layout ........................................................................................................ ll4

Figure 5.2: Transmission and differential finite element layout ............................................................... 126

Figure 5.3: Linearised damping for even gears ......................................................................................... l27

Figure 5.4: Linearised data for odd gears ................................................................................................. 127

Figure 5.5: Linearised data for coupling drag ........................................................................................... l28

Figure 5.6: Linearised data for final drive I ............................................................................................. 128

Figure 5.7: Linearised data for final drive 2 ............................................................................................. 128

Xlll

Figure 5.8: highlighted sources of drag torque that will affect the synchronisation of 2nd 4th and 6th gears

.................................................................................................................................................................. 130

Figure 5.9: Synchronisation time for upshifts and downshifts ................................................................. 133

Figure 5.10: Synchronisation energy for upshifts and downshifts ........................................................... 133

Figure 5.11: Assumed and numerical mean drag torques at the synchroniser .......................................... 134

Figure 5.12: Unblocking time variation based on different drag torques ................................................. 134

Figure 5.13: Drag torques for a 3-4 upshift. (a) Synchroniser sleeve displacement, (b) absolute drag

torque, (c) relative drag torque ................................................................................................................. 135

Figure 5.14: Drag torques for a 5-4 downshift. (a) Synchroniser sleeve displacement, (b) absolute drag

torque, (c) relative drag torque ................................................................................................................. 136

Figure 5.15: Drag torques developed during synchronisation for downshifts .......................................... 137

Figure 5.16: Drag torques developed during synchronisation for upshifts ............................................... 138

Figure 6.1: Example of good and poor chamfer alignments during synchroniser engagement... ............. 142

Figure 6.2: Example of tip-on-tip alignment condition ............................................................................ 143

Figure 6.3: Demonstration of different alignment issues for wet clutches, fourth gear is synchronised with

third gear engaged (top) and fifth gear engaged (bottom) ........................................................................ 144

Figure 6.4: Demonstration of different alignment issues for dry clutches, fourth gear is synchronised with

third gear engaged (top), and fifth gear engaged (bottom) ....................................................................... 145

Figure 6.5: Synchroniser engagement override control algorithm ........................................................... 147

Figure 6.6: Sleeve displacement results for closed loop alignment control of wet clutches for upshift (top)

and downshift (bottom) ............................................................................................................................ 148

Figure 6.7: Active and idle cylinder pressures for closed loop alignment control of wet clutches for

upshift (top) and downshift (bottom) ....................................................................................................... 149

Figure 6.8: Sleeve displacement results for closed loop alignment control of dry clutches for upshift (top)

and downshift (bottom) ............................................................................................................................ 150

Figure 6.9: Active and idle cylinder pressures for closed loop alignment control of dry clutches for upshift

(top) and downshift (bottom) ................................................................................................................... 150

Figure 6.10: Schematic for Case 1, external excitation through an applied torque .................................. 153

Figure 6.11: control of chamfer alignment in a wet clutch DCT using an externally applied torque for


Figure 6.12: Control of chamfer alignment in a dry clutch DCT using an externally applied torque for


Figure 6.13: Example model oflnertia change system for Case 2 ........................................................... 156

Figure 6.14: Control of chamfers for a wet clutch DCT using torque impulse for upshift (top) and

downshift (bottom) ................................................................................................................................... 158

XIV

Figure 6.15: Control of chamfers for a dry clutch DCT using torque impulse for upshift (top) and

downshift (bottom) ................................................................................................................................... 158

Figure 6.16: Detailed cross section of double contact thrust piece ........................................................... 160

Figure 6.17: Simulations of engagement with double contact thrust piece in wet clutch DCT, (top)

upshifts and (bottom) downshifts ............................................................................................................. 161

Figure 7.1: Synchroniser engagement simulations with variation to the cone clutch mean radius, (top)

Cone clutch slip speed during synchronisation of gear, and (bottom) sleeve displacement simulation ... 167

Figure 7.2: sleeve displacement variation with chamfer angle and pitch radius change .......................... 169

Figure 7.3: dimensionless chamfer torque as a function of chamfer angle and operating radius ............. 169

Figure 7.4: Variation of sleeve displacement with modification to the chamfer pitch radius and number of

chamfers at a chamfer angle of 50 degrees ............................................................................................... 170

Figure 7.5: Variation of sleeve displacement with modification to the chamfer angle at a constant pitch

radius of 40mm ......................................................................................................................................... 170

Figure 7.6: Synchroniser engagement simulations with variation to chamfer design according to Table 2,

(top) cone clutch slip speed, and (bottom) Sleeve displacement .............................................................. 171

Figure 7.7: Typical section of inverted synchroniser mechanism ............................................................. 173

Figure 7.8: Detail of thrust piece and detents ........................................................................................... 173

Figure 7.9: Detailed thrust piece positions, from left to right (1) neutral position, (2) at end of initial

displacement before sleeve and ring chamfers engaged, (3) During synchronisation with sleeve and ring

chamfers engaged and thrust piece detent retracted, and (4) at full displacement with thrust piece dented

fully retracted and gear completely engaged ............................................................................................ 174

Figure 7.10: Simulations of the inverted cone synchroniser mechanism, (top) above 3rd to 4th gear

synchronisations, and (bottom) below 5th to 4th gear synchronisations .................................................. 176

Figure 8.1: Semi-definite two degree of freedom system ......................................................................... 180

Figure 8.2: Layout of dual clutch transmission ......................................................................................... 184

Figure 8.3: Simplified powertrain dynamic model with clutches and synchronisers ................................ 186

Figure 8.4: Engine, flywheel, and clutch drum model elements ............................................................... 186

Figure 8.5: Dual mass flywheel elements ................................................................................................. 187

Figure 8.6: Clutch and simple transmission model e1ements .................................................................... l89

Figure 8.7: final drive and reduced differential model elements .............................................................. 191

Figure 8.8: Shafts model elements ............................................................................................................ l92

Figure 8.9: Differential and axle elements ................................................................................................ l93

Figure 8. 10: Hub and tyre model elements ............................................................................................... 193

Figure 8.11: Engine torque map ............................................................................................................... 200

Figure 8.12: 5 degree of freedom transient engine torque model ............................................................. 201

XV

Figure 8.13: Piston head pressure map over 4 strokes ............................................................................. 203

Figure 8.14: Transient engine torque simulation results .......................................................................... 203

Figure 8.15: Calculated cylinder pressures for assumed 0% and 10% throttle angles ............................. 204

Figure 9.1: General DCT powertrain layout ............................................................................................. 213

Figure 9.2: 4DOF model ofpowertrain with both clutches open ............................................................. 215

Figure 9.3: 3DOF dynamic model ofpowertrain with clutch one closed ................................................. 215

Figure 9.4: friction coefficient representation as a function of slip speed ................................................ 217

Figure 9.5: Simulink- Stateflow representation of reduced order powertrain with integrated control

modules .................................................................................................................................................... 218

Figure 9.6: Powertrain control logic ......................................................................................................... 224

Figure 9.7: Sensitivity study of clutch torque response to variation in estimated torque ......................... 225

Figure 9.8: Typical torque profiles of both clutches during shifting ........................................................ 226

Figure 9.9: Engine control methods. Showing both speed control (left) and torque control (right) ........ 230

Figure 9.10: Engine control responses from simulation showing throttle angle (above) and engine speed

(below) ..................................................................................................................................................... 231

Figure 9.11: Clutch control responses, showing control signal (top), spool position (middle), and clutch

pressure (bottom) ..................................................................................................................................... 232

Figure 9.12: Simulation results for a 3-4 up-shift showing speeds for (a) Clutch drum and clutch 2, (b)

vehicle acceleration, and (c) clutch pressures during shifting using ideal clutch torques ........................ 234

Figure 9.13: Simulation results for a 3-4 up-shift with minimised time delay showing speeds for (a) clutch

drum and clutch 2, (b) vehicle acceleration, and (c) clutch pressures during shifting using engine speed

control and Clutch 2 average torque estimation ....................................................................................... 235

Figure 9.14: Simulation results for a 3-4 up-shift showing speeds for (a) clutch drum and clutch, (b)

vehicle acceleration and (c) clutch pressures during shifting using engine speed and torque control, and

clutch 2 average torque estimation ........................................................................................................... 237

Figure 9.15: Simulation results for a 3-4 up-shift with variance in estimated torque for controller input

showing speeds for (a) clutch drum and clutch, (b) vehicle acceleration, and (c) clutch pressures ......... 238

Figure 9.16: Gear shift simulation results for 3nl to 4th upshift using 4DOF model with transient engine

torque, (a) clutch drum and hub speeds, and (b) clutch 2 output and total vehicle torques ...................... 240

Figure 9.17: Gear shift simulation results for 3nl to 41h upshift using 4DOF model with transient engine

torque, (a) clutch drum and hub speeds, and (b) clutch 2 output and total vehicle torques ...................... 242

Figure I 0.1: Synchroniser sleeve displacement for rigid body model and lumped mass model engagement

simulations ............................................................................................................................................... 247

Figure 10.2: Synchroniser engagement responses, showing (top) sleeve displacement during engagement

and, (bottom) effective synchroniser torque ............................................................................................. 248

Figure 10.3: Synchroniser hub and sleeve speeds (top), and synchroniser relative speed (bottom) ......... 250

XVI

Figure 10.4: Cone slip speed demonstrating stick- slip during final stages of speed synchronisation .... 250

Figure 10.5: Synchroniser engagement responses using dynamic engine model, showing (top) sleeve

displacement during engagement and, (bottom) effective synchroniser torque ........................................ 251

Figure 10.6: Synchroniser hub and sleeve speeds (top), and synchroniser relative speed (bottom) using

dynamic engine model .............................................................................................................................. 252

Figure 10.7: Demonstration of stick-slip phenomena using a dynamic engine model ............................. 253

Figure 10.8: Relative vibration synchroniser sleeve during actuation of the synchroniser mechanism. For

the ideal engine models (a) during synchronisation and (b) during indexing, and using the unsteady

engine model (c) during synchronisation and (d) during indexing ........................................................... 254

Figure l 0.9: Fast Fourier Transforms of sleeve relative vibration during synchronisation ...................... 255

Figure 10.10: Enlarged view ofFFT results in figure 10.9, focus on frequencies less than 500Hz ......... 255

Figure 10.11: Clutch 1, clutch 2, and throttle angle control signals (arrows used to indicate different steps

of the shift process) ................................................................................................................................... 256

Figure 10.12: Gear shift simulation results for 3rd to 4th upshift using 4DOF model with mean engine

torque, (a) clutch drum and hub speeds, and (b) clutch 2 and vehicle torques ......................................... 258

Figure 10.13: Gear shift simulation results for 3'd to 4th upshift using 15DOF model with mean engine


Figure 10.14: Gear shift simulation results for 3rd to 4th upshift using 15DOF model with transient engine


Figure 10.15: Clutch 1 slip speed showing stick slip introduced during pre-shift period in the 15DOF

powertrain with transient torque model .................................................................................................... 261

Figure 10.16: Gear shift simulation results for 3rd to 4th upshift using 15DOF model with transient engine

torque and linearised DMFW, (a) clutch drum and hub speeds, and (b) clutch 2 and vehicle torques ..... 262

Figure I 0.17: Linear shift process in DCTs .............................................................................................. 262

Figure 10.18: combined shift transient engine and clutch I and 2 control signals ................................... 263

Figure 10.19: combined 4th gear synchronisation and upshift from 3rd to 4th gear simulation ................. 264

Figure 10.20: Stick-slip simulations (a) drum speed, (b) clutch I stick-slip ............................................. 265

Figure 10.21: acceleration of clutch 2 hub at different stages of synchronisation and gearshift (a) during

speed synchronisation, (b) completion of synchronisation, (c) during clutch-to-clutch shift, and (d) after

lockup ....................................................................................................................................................... 266

Figure 11.2: mesh contact model for synchroniser splines ....................................................................... 272

Figure 11.1: Transmission lumped inertia model ..................................................................................... 272

Figure 11.3: Mesh contact model for gear pair ......................................................................................... 273

Figure 11.4: Mesh stiffness model for gear and synchroniser contact nonlinearity ................................. 274

Figure 11.5: Shift control signals for transient simulations ...................................................................... 277

Figure 11.6: Synchroniser sleeve displacement (top) and engagement torque (bottom) ......................... 278

xvn

Figure 11.7: Synchroniser hub and sleeve speeds (top), and synchroniser relative speed (bottom) ......... 278

Figure 11.8: Phase plots of target gear mesh during different stages of synchronisation. (a) during speed

synchronisation, (b) during ring unblocking, (c) during second displacement, and (d) during indexing.

The hexagram indicates the starting point. ............................................................................................... 279

Figure 11.9: Shift transient simulations with nonlinear gear and synchroniser mesh, clutch hub and drum

speeds (a), and clutch 2 and net vehicle torque (b) .................................................................................. 280

Figure 11.10: Stick slip present in clutch 2 at lockup .............................................................................. 281

Figure 11.11: Mesh relative displacement plots of both gears during shift transients ............................. 282

Figure 11.12: Mesh relative displacement plots of both synchronisers during shift transients ................ 282

Figure 11.13: Throttle angle tip-in/tip-out according to equation 11.19 ................................................. 283

Figure 11.14: Time history of tip-in/tip-out simulation with mean engine torque model ........................ 284

Figure 11.15: Relative displacement plots of (a) Gear 1 and (b) synchroniser 1 during throttle

manipulation for tip-in/tip-out simulations with mean engine torque model ........................................... 285

Figure 11.16: Relative velocity-displacement phase plots of (a) Gear 1 and (b) Synchroniser 1 during the

lash period with the mean engine torque model ....................................................................................... 285

Figure 11.17: Time history of tip-in/tip-out simulation with harmonic engine torque model .................. 286

Figure 11.18: First lash transitions for (a) gear 1 with harmonic engine model, (b) gear 1 with mean

engine model, (c) synchroniser 1 with harmonic engine model, and (d) synchroniser 1 with mean engine

model ........................................................................................................................................................ 287

Figure 12.1: Failed simulation of combined synchroniser engagement and gearshift ............................. 297

XVlll

LIST OF TABLES Table 3.1: Hydraulic model parameters ...................................................................................................... 54

Table 3.2: Synchroniser hydraulic system properties ................................................................................. 67

Table 4.1: Synchroniser model parameters ................................................................................................ 92

Table 4.2: Steady state gear speeds for engaged speed of 1500RPM (157.1 rad/s) .................................... 92

Table 4.3: ATF parameters ....................................................................................................................... 100

Table 4.4: Parameters and initial conditions for parameter variation simulations .................................... 1 08

Table 5.1: Drag torque data for gear modelling ........................................................................................ 125

Table 5.2: Summary of damping coefficients ........................................................................................... 129

Table 6.1: Simulation model properties for excitation method ................................................................. 157

Table 7.1: Simulation parameters ............................................................................................................. 171

Table 7.2: Inverted cone design simulation parameters and dimensionless parameters ........................... 175

Table 8.1: System states for shifting of DCT, "0" signifies open, "X" signifies closed .......................... 185

Table 8.2: Transmission and final drive gear ratios .................................................................................. 194

Table 8.3: Powertrain parameters to be applied to the nDOF models ...................................................... 195

Table 8.4: Free vibration analysis of powertrain with 3rd gear and clutch 1 engaged, synchroniser two

engaged with 4th gear. Results show natural frequencies, damping ratios and modal shapes .................. l98

Table 8.5: Free vibration analysis of powertrain with 4th gear and clutch 2 engaged, synchroniser one

engaged with 3rd gear. Results show natural frequencies, damping ratios and modal shapes .................. 199

Table 8.6:Transient engine model parameters .......................................................................................... 201

Table 9.1: Natural frequencies and damping ratios for parameter estimation, for clutch 1 in 3rd gear and

clutch 2 in 4th gear ................................................................................................................................... 218

Table 9.2: Estimated system parameters for a 3rd to 41h gear upshift ........................................................ 220

Table 9.3: 4DOF and 15DOF system natural frequencies ........................................................................ 221

Table 9.4: Normalised modal shapes and natural frequencies of 4DOF model engaged in 3rd gear ......... 222

Table 9.5: First four normalised modal shapes and natural frequencies of the 15DOF system engages in

3rd gear ...................................................................................................................................................... 223

Table 11.1: Nonlinear contact model parameters ..................................................................................... 276

GLOSSARY OF TERMS AND NOTATION

DCT

MT

AMT

AT

CVT

TCU

DOF

VFS

NVH

DMFW

1

t

A

cd Co

D

F

Ks

M

p

Q

V

X

x

ABBREVIATIONS USED IN THIS THESIS

Dual clutch transmission

Manual transmission

Automated manual transmission

Automatic transmission

Continuously variable transmission

Transmission control unit

Degrees of freedom

Variable force solenoid

Noise vibration and harshness

Dual mass flywheel

CHAPTER 3 NOTATION

General

Bulk modulus

Viscosity

Radial clearance

Sliding contact length

Time

Cross-sectional area

Damping coefficient

Discharge coefficient

Diameter

Force

Spring constant

Mass

Pressure

Flow rate

Volume

Displacement

Velocity

XIX

0

syn

c Cl

CV##-

Exh

IN

L

MMF-

0

p

V

a

p 0

So

e" Bs

(}FW

(}R

~

~c

~.s

fJDETENT

fJI

fJR

A.

Acceleration

Subscripts

initial condition

synchroniser

Cylinder

Clutch

Control volume number for fluid system

Exhaust

Inlet

Leak

Magneto-motive force

Orifice

Piston or spool

Volume

Cone angle

Chamfer angle

CHAPTER 4 NOTATION

Angular displacement between consecutive chamfers

Detent contact angle

Chamfer relative alignment

Cone relative speed

Freewheeling component acceleration

Ring acceleration

Transmission fluid viscosity

Cone dynamic friction

Cone static friction

Detent friction coefficient

Chamfer friction coefficient

Ring/sleeve sliding friction

Chamfer flank contact

XX

n A

a

b

h

Xs

FA

FoETENT

FFILM -

Fwss -

FR

IFW

IR

lv

KoR

NCH

Re

RH

RI

Rm

RR

Ts

Tc

To

TI

Ts

Tv

Dimensionless group

Empirical constant that is dependent on the lubrication case (l>A>5)

Grooved width

Semi-width of the contact generatrix in the cone [66]

Film thickness

Sleeve mass

Sleeve and ring mass

Number of grooves

Unblocking time

Synchronisation time

Sleeve displacement

Sleeve acceleration

Net sleeve load

Detent force

film squeezing force

Seel drag losses

Radial force

Inertia of the freewheeling components

Inertia of the ring

Vehicle inertia

Groove coefficient

Number of chamfers on one ring

Mean cone radius

RMS roughness of the hub

Pitch radius of chamfers

Cone mean radius

RMS roughness of the ring

Blocking torque

Cone torque.

Drag torque

Indexing torque

Synchronisation torque

Vehicle torque

xxi

V

!l

p

w

roo

~ffiCL -

e b

d

f

h

r

c E

Gr

H

H

IFW

KE

M

N

p

Re

Q

T

X

z

CHAPTER 5 NOTATION

General

transverse operating pressure angle

operating helix angle

gear ratio

kinematic viscosity

dynamic viscosity

density

rotational velocity

Gear speed

Clutch slip speed

Rotational displacement

Face width

Diameter

Friction

Fluid spacing

Radius(* denotes radius at critical Reynolds number)

Drag torque dimensionless coefficient

Energy

Turbulent flow coefficient

Sliding ratio at the start of the approach

Sliding ratio at the end of the recess

Reflected inertia

Kinetic energy

Mesh mechanical advantage

rotational speed (RPM)

Mesh power loss (kW)

Reynolds number (* denotes critical Reynolds number)

Flow rate

Torque

Profile coefficient

module

Subscripts

XXll

ol

o2

s

t

wl

w2

A

B

CL

D

F

I

M

0

p

SH

V

w

pinion outside radius

gear outside radius

Start of approach

End of approach

pinion operating pitch radius

gear operating pitch radius

Tooth tip

Bearing losses

Clutch windage

Drag

Gear friction

Inside

Mesh

Outside

Pitch point

Inter-shaft shear

windage

Gear windage

CHAPTER 6 NOTATION*

Se

8p

*Any previously used terminology can be found in Chapter 4 or 5 notation

Control system rotation DOF

le

lp

Ke

TeoNT -

TsvN -

Xe

11xs

Pinion DOF

Control system inertia (0 for initial, 11 for change in inertia)

Pinion inertia

Control shaft stiffness

Control torque

Synchroniser torques

Chamfer contact displacement

Net sleeve displacement over one chamfer

CHAPTER 7 NOTATION*

XXlll

*Any previously used terminology can be found in Chapter 4, 5 or 6 notation

R Cone radius

r

8

iJ

iJ

'}'

(0

X

x X

T

c I

K

M

T

X

I

2

e

hys

AX

c DIFF -

F

DM

FD

Chamfer pitch radius

CHAPTER 8 NOTATION

General

Angular displacement

Angular velocity

Angular acceleration

Gear ratio

Frequency

Phase angle

Damping ratio

Displacement

Velocity

Acceleration

Time

Damping coefficient

Inertia

Spring coefficient

Mass

Torque

Amplitude coefficient

Subscripts

Refers to components associated with odd gears

Refers to components associated to even gears

Engine

Hysteresis

Axle

Clutch

Differential

Flywheel or Dual mass flywheel primary

Clutch drum or Dual mass flywheel secondary integrated with clutch

Final drive

xxiv

G

p

s SL

T

w

8

ffie

mT

Ap

Mp

p

R

s T

Tp

Tt

V

n

Tavg

X

Xo

Gear

Pinion

Synchroniser

Synchroniser sleave

Tyre

Wheel hub

Engine models

Crank angle

Engine speed

Mass of gas

Piston area

Piston mass

Instantaneous piston pressure

Ideal gas constant

Piston speed

Piston temperature

Piston torque

Inertia change torque

Piston volume

Clutch model

Dynamic friction coefficient

Static friction coefficient

Clutch slip speed

Number of friction surfaces

Inside radius

Outside radius

Axial force

Clutch torque

Average torque

Piston displacement

Contact displacement for friction plates

XXV

Synchroniser model

Refer to Chapter 4 notation

eincline -

Pair

g

Co

Ctire

Faero

Fincline -

Froll

FR

Hv

Mv

Rwheel -

TR

Vw

Wv

Vehicle torque model

Angle of inclination

Air density

Gravity

Coefficient of drag

Dimensionless tire retarding force

Aerodynamic drag load

Incline load

Aerodynamic drag load

Net resistance force

Vehicle height

Vehicle mass

Wheel radius

Net resistance torque

Linear velocity of driving wheels

Vehicle width

CHAPTER 9 NOTATION

*Any previously used terminology can be found in Chapter 8 notation

® - Amplitude coefficient

C- Clutch

D - clutch drum

E-Engine

T- Transmission

V- Vehicle

General

Subscripts

xxvi

1,2 - clutch or gear number

CHAPTERllNOTATION

*Any previously used terminology can be found in Chapter 8 notation

e -rotational degree of freedom

Se- Contact displacement rotation

C-Damping

I- Inertia

K - stiffness

M-Mass

r-radius

t -time

TA - throttle angle

x - gear linear degree of freedom

Xc - contact displacement length

y - pinion linear degree of freedom

B -Bearing

Refer to Chapter 8 subscripts

General

Subscripts

xxvii

XXVlll

ABSTRACT Transient dynamic investigations of dual clutch transmission equipped powertrains are

conducted in this thesis through the development and application of torsional multi

body models incorporating multiple nonlinearities. Shift control studies are performed

using detailed hydraulic model integrated with a 4DOF powertrain model. Results

illustrate that accuracy of torque estimation, time delay in engine and clutches, and

torque balance in the powertrain all influence the shift quality. Powertrain transient

studies have been carried out to investigate the impact of multiple nonlinearities on

powertrain dynamics and shift quality. This makes use of the clutch friction stick-slip

algorithm to model nonlinearity in clutch engagements, with other nonlinearities

including mean and harmonic engine torque models and dual mass flywheel with

hysteresis. Comparisons between 4 and 15 DOF powertrain models are made, and the

impact of using engine harmonics for the DCT powertrain identified. Results of these

studies are also discussed with respect to stick-slip response clutches and the effect on

post shift transient response. Finally, a backlash model is introduced for gears and

synchronisers to study response under a variety of operating conditions, including

synchroniser engagement, shift transients and engine tip-in/tip-out.

Investigations of synchroniser mechanism dynamics and control are undertaken with a

rigid body mechanism model, and as part of the DCT powertrain using a 15 DOF multi

body model. Broad ranging parameter studies are undertaken for design and

environmental variables that impact on synchroniser performance, and dimensionless

torques are introduce for the study of synchroniser design parameters. Slip regeneration

is identified as a significant issue in mechanism actuation, in terms of engagement

repeatability and damage to chamfer friction surfaces. Alignment control methods are

studied to attempt to reduce the impact of chamfer alignment and regenerated slip on

engagement performance. Finally two design modifications are suggested for the

mechanism to eliminate the slip issue, and provide higher synchroniser torques for a

similar design envelope. Powertrain simulation results suggest that under nominal

actuation, using the mean engine torque model, vibrations of the sleeve increase during

indexing alignment of chamfers, indicating increased wear of friction surfaces. With

the inclusion of the harmonic engine torque model, vibrations in the transmission

increases significantly throughout the engagement process; however these results do not

indicate that there is an increased likelihood of clash during speed synchronisation.

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